Vector Algebra Question 318
Question: The vectors a and b are non-collinear. The value of x for which the vectors $ \mathbf{c}=(x-2),\mathbf{a}+\mathbf{b} $ and $ \mathbf{d}=(2x+1),\mathbf{a}-\mathbf{b} $ are collinear, is
Options:
A) 1
B) $ \frac{1}{2} $
C) $ \frac{1}{3} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- Since $ \mathbf{c}=(x-2)\mathbf{a}+\mathbf{b} $ and $ \mathbf{d}=(2x+1)\mathbf{a}-\mathbf{b} $ are collinear, therefore $ \mathbf{c}=\lambda \mathbf{d} $
$ \Rightarrow (x-2)\mathbf{a}+\mathbf{b}=\lambda (2x+1)\mathbf{a}-\lambda \mathbf{b} $ or $ [(x-2)-\lambda (2x+1)]\mathbf{a}+(\lambda +1)\mathbf{b}=0 $ $ (x-2)-\lambda (2x+1)=0,\lambda +1=0 $ $ (\because ,\mathbf{a},,\mathbf{b} $ are linearly independent)
$ \Rightarrow x-2+2x+1=0\Rightarrow x=\frac{1}{3}. $
BETA
